Two-dimensional Gaussian Function
In two dimensions, the power to which e is raised in the Gaussian function is any negative-definite quadratic form. Consequently, the level sets of the Gaussian will always be ellipses.
A particular example of a two-dimensional Gaussian function is
Here the coefficient A is the amplitude, xo,yo is the center and σx, σy are the x and y spreads of the blob. The figure on the right was created using A = 1, xo = 0, yo = 0, σx = σy = 1.
In general, a two-dimensional elliptical Gaussian function is expressed as
where the matrix
is positive-definite.
Using this formulation, the figure on the right can be created using A = 1, (xo, yo) = (0, 0), a = c = 1/2, b = 0.
Read more about this topic: Gaussian Function
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